Reversible quaternionic hyperbolic isometries

Abstract

Let Gbe a group. An element g∈Gis called reversibleif it is conjugate to g−1within G, and called strongly reversibleif it is conjugate to g−1by an order two element of G. Let HnHbe the n-dimensional quaternionic hyperbolic space. Let PSp(n, 1) be the isometry group of HnH. In this paper, we classify reversible and strongly reversible elements in Sp(n)and Sp(n, 1). Also, we prove that all the elements of PSp(n, 1)are strongly reversible.